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Size Effects in Meso- and Microscaled Forming
Published in Xin Min Lai, Ming Wang Fu, Lin Fa Peng, Sheet Metal Meso- and Microforming and Their Industrial Applications, 2018
Xin Min Lai, Ming Wang Fu, Lin Fa Peng
Surface layer model assumes that the workpiece to be deformed consists of the surface layer and the inner part. As shown in Figure 2.5, the surface layer has the thickness of one grain diameter and the remaining grains are the inner part of the workpiece. Compared with the inner grains, the surface layer grains are located at the free surface and thus have less restriction. It is harder for dislocations to pile up at grain boundaries when moving through the surface grains. Therefore, surface grains have less hardening and low resistance against deformation. In meso- and microforming, with the increase in miniaturization, the increase of the share of surface grains thus results in the decrease of flow stress of materials. Therefore, the size effect thus occurs as the geometry size affects the material deformation behaviors.
Critical Issues in Small Specimen Testing
Published in V. Karthik, K.V. Kasiviswanathan, Baldev Raj, Miniaturized Testing of ENGINEERING MATERIALS, 2016
V. Karthik, K.V. Kasiviswanathan, Baldev Raj
Mechanical properties change drastically when the specimen dimensions are small and the term “size effect” is used generically to describe this. The size effect manifests as the specimen dimensions approach the length scales of the defects controlling the deformation where the laws of continuum mechanics are no longer valid. This is true for materials in miniaturized devices used in the form of thin films, whose dimensions become comparable to the microstructural length scale. In such cases, the aim is to evaluate the mechanical response of materials at length scales comparable to those used in actual application. The small size specimens are close to reality when coatings, thin films, microelectromechanical structure, or materials for such applications are tested and evaluated, as illustrated in Figure 4.1.
Rate effects in fracture of concrete and size dependence
Published in Günther Meschke, René de Borst, Herbert Mang, Nenad Bićanić, Computational Modelling of Concrete Structures, 2020
The size effect is understood as the dependence of the structural strength on the structural size. The nominal strength is conventionally defined as the value of the so-called nominal stress at the peak load Fmax (Bazant & Planas 1998) calculated as: σNu=cNFmaxbD where b is the specimen thickness (b = 1) and cn is a coefficient introduced for convenience (cN = 1.5). The nominal strength σNu is computed versus the size D. In a log-log plot, the nominal strength law obtained with the coupled damage-viscoplasticity model can be drawn versus size D as shown in Figure 8. We can observe a clear trend of σNu which is dependent on size D. Agreement of the model response with the well-known size effect law given by Equation 5 is clear. The values of the parameters Bft′. and D0 of this law are obtained by optimal least-square fitting of the Bazant’s size effect law with the numerical results. The asymptote of the Bazant’s size effect law for large size is consistent with material developing a brittle behavior.
Fiber orientation effects on the non-linear vibrations for a microstructure-dependent tapered plate containing an arbitrarily located crack
Published in Mechanics Based Design of Structures and Machines, 2023
Bhupesh Kumar Chandrakar, N. K. Jain, Ankur Gupta
An additional internal material length scale parameter is considered to incorporate the size-effect. It is seen that as the size of the internal material length scale parameter increases, the fundamental frequency also increases. Hence, the present model can easily be applied to understand the frequency behavior of micro-sized orthotropic plates. To make the model more practical, the mathematical model is also extended to understand the influence of the taper parameter on the nonlinearity of the orthotropic tapered plate using the method of multiple scales. Non-linearity decreases with increasing the taper parameter and the fiber direction for both x and y-direction with the linear thickness variation. The plate with the SSSS boundary condition is seen to be more non-linear as compared to the CCSS boundary condition.
Efficient Constitutive Model for Continuous Micro-Modeling of Masonry Structures
Published in International Journal of Architectural Heritage, 2023
M. Petracca, G. Camata, E. Spacone, L. Pelà
Homogenous continuum models (Pelà et al. 2014; Pelà, Cervera, and Roca 2011, 2013) can be used in a standard macroscopic approach, where the whole masonry structure is modeled as an equivalent homogeneous medium equipped with an equivalent homogeneous material that should be able to represent the main features of masonry. This method is the fastest in terms of both computational costs and model complexity. However, simple tensorial constitutive models may not be able to accurately represent features such as strength orthotropy followed by damage-induced anisotropy and the effects of the arrangement and size of micro-structural constituents. Furthermore, it is well known that standard tensorial constitutive models, either based on plasticity, damage, or a combination of them, fail in representing the so-called “size effect” (Barenblatt 2014; Bažant 2004). A “size effect” arises every time a material property does not appear to be the same for two geometrically similar structures with different sizes: In quasi-brittle materials, in fact, both structural brittleness and material strength are found to be scale-dependent.
Size effect on compressive behaviors of waste fiber-reinforced recycled aggregate concrete
Published in European Journal of Environmental and Civil Engineering, 2022
Tianbei Kang, Songxu Li, Liwei Jin, Xiaoxin Wu, Jinghai Zhou, Yichao Zhang, Yibo Liang
Size effect means that the mechanical properties of materials or components represented by nominal strength tend to decrease with the increase of geometric size, which is the inherent characteristic of brittle materials. Concrete is a typical quasi-brittle material; apart from various factors such as aggregate composition and mix ratio, the change of geometric size also affects concrete strength (Chen et al., 2018; Su & Fang, 2013), as shown in Figure 1 (Du et al. 2017). When compared with the size effect on concrete or concrete structural members, only a few references (Fládr & Bílý, 2018; Kazemi & Lubell, 2012; Nguyen et al., 2013) are available regarding the size effect of fiber-reinforced concrete or fiber-reinforced recycled concrete. Nguyen et al. (2013) investigated the size effect on the flexural behavior of ultra-high-performance hybrid fiber-reinforced concrete (UHP-HFRC); they reported that the flexural behavior of UHP-HFRC, with its lower tensile ductility, was more sensitive to the size of the specimen. Fládr and Bílý (2018) stated that the compressive strength of high-strength fiber-reinforced concrete with coarse aggregate generally decreases with increasing cube size. Moreover, for each type of concrete, the relation between the size of the specimen and measured strength has to be derived experimentally; Kazemi and Lubell (2012) got the same conclusion.